Recursive all-lag reference-code correlators

Abstract

An all-lag reference-code correlator generates an all-lag even-or odd-correlation vector at a rate equal to the rate of incoming data samples. Direct implementation of an all-lag reference-code correlator requires N parallel correlators, and the resultant degree of complexity is of the order N2, where N is the length of the reference code. This paper derives two recursive forms for all-lag reference-code correlators. One generates all-lag even correlation and the other one generates all-lag odd correlation. It is shown that the proposed recursive all-lag reference-code correlator can be implemented with a complexity approximately equal to that of a single parallel correlator. That is, the degree of complexity of the proposed recursive all-lag reference-code correlator is of the order N. Thus, substantial reduction in the implementation complexity is achieved.